{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:75JBUGUZKTGTZWV6TFWHXRYPGL","short_pith_number":"pith:75JBUGUZ","schema_version":"1.0","canonical_sha256":"ff521a1a9954cd3cdabe996c7bc70f32f0cef0f00ace58215d9b1fc27c84da5d","source":{"kind":"arxiv","id":"1508.07295","version":2},"attestation_state":"computed","paper":{"title":"The $F$-different and a canonical bundle formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Karl Schwede, Omprokash Das","submitted_at":"2015-08-28T17:58:33Z","abstract_excerpt":"We study the structure of Frobenius splittings (and generalizations thereof) induced on compatible subvarieties $W \\subseteq X$. In particular, if the compatible splitting comes from a compatible splitting of a divisor on some birational model $E \\subseteq X' \\to X$ (ie, this is a log canonical center), then we show that the divisor corresponding to the splitting on $W$ is bounded below by the divisorial part of the different as studied by Kawamata, Shokurov, Ambro and others. We also show that difference between the divisor associated to the splitting and the divisorial part of the different "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1508.07295","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-28T17:58:33Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"185178d958ece20e6193b3868980606bdabd010a08828036bbaaaa2f5fd25d8a","abstract_canon_sha256":"f5633641f9edf9a5d543d0d3fdea9e6d33bbe2d952ec8427a074880c756f2c3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:43.856870Z","signature_b64":"IbXwsmrFb18WJ8WXdl2JILmD2V0hIR4Uwv8pTbrmXyzDOme1D+a2+1+fSXzEL2cnoozrqFm7SoSZD+f3ypfjAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff521a1a9954cd3cdabe996c7bc70f32f0cef0f00ace58215d9b1fc27c84da5d","last_reissued_at":"2026-05-17T23:42:43.856111Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:43.856111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $F$-different and a canonical bundle formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Karl Schwede, Omprokash Das","submitted_at":"2015-08-28T17:58:33Z","abstract_excerpt":"We study the structure of Frobenius splittings (and generalizations thereof) induced on compatible subvarieties $W \\subseteq X$. In particular, if the compatible splitting comes from a compatible splitting of a divisor on some birational model $E \\subseteq X' \\to X$ (ie, this is a log canonical center), then we show that the divisor corresponding to the splitting on $W$ is bounded below by the divisorial part of the different as studied by Kawamata, Shokurov, Ambro and others. We also show that difference between the divisor associated to the splitting and the divisorial part of the different "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07295","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1508.07295","created_at":"2026-05-17T23:42:43.856236+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.07295v2","created_at":"2026-05-17T23:42:43.856236+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07295","created_at":"2026-05-17T23:42:43.856236+00:00"},{"alias_kind":"pith_short_12","alias_value":"75JBUGUZKTGT","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"75JBUGUZKTGTZWV6","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"75JBUGUZ","created_at":"2026-05-18T12:29:07.941421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/75JBUGUZKTGTZWV6TFWHXRYPGL","json":"https://pith.science/pith/75JBUGUZKTGTZWV6TFWHXRYPGL.json","graph_json":"https://pith.science/api/pith-number/75JBUGUZKTGTZWV6TFWHXRYPGL/graph.json","events_json":"https://pith.science/api/pith-number/75JBUGUZKTGTZWV6TFWHXRYPGL/events.json","paper":"https://pith.science/paper/75JBUGUZ"},"agent_actions":{"view_html":"https://pith.science/pith/75JBUGUZKTGTZWV6TFWHXRYPGL","download_json":"https://pith.science/pith/75JBUGUZKTGTZWV6TFWHXRYPGL.json","view_paper":"https://pith.science/paper/75JBUGUZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.07295&json=true","fetch_graph":"https://pith.science/api/pith-number/75JBUGUZKTGTZWV6TFWHXRYPGL/graph.json","fetch_events":"https://pith.science/api/pith-number/75JBUGUZKTGTZWV6TFWHXRYPGL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/75JBUGUZKTGTZWV6TFWHXRYPGL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/75JBUGUZKTGTZWV6TFWHXRYPGL/action/storage_attestation","attest_author":"https://pith.science/pith/75JBUGUZKTGTZWV6TFWHXRYPGL/action/author_attestation","sign_citation":"https://pith.science/pith/75JBUGUZKTGTZWV6TFWHXRYPGL/action/citation_signature","submit_replication":"https://pith.science/pith/75JBUGUZKTGTZWV6TFWHXRYPGL/action/replication_record"}},"created_at":"2026-05-17T23:42:43.856236+00:00","updated_at":"2026-05-17T23:42:43.856236+00:00"}